Hate it when kids show up to class with math tricks that
shortcut real concept development?

When a colleague approached her to lament their students' grasp
of slope, Tina Cardone expanded the conversation -- first to
her math department, then to her online community. By sharing
methods that emphasize understanding over memorization,
together they have developed a group document of the "worst
offenders" to nix -- and their fixes.

Named after the sixth Math Practice of the Common Core State
Standard (CCSS), the current draft of "Attend to Precision" has
four themes: phrases to avoid, vocabulary, notation, and
"debate!" Mnemonics, cliches, and other tricks to nix and
fix include

Evaluating Expressions: PEMDAS

Evaluating Expressions: Two negatives make a positive

Less Than/Greater Than: "Hungry" symbols

What's the first step?

Operations with Fractions: Cross multiply

Multiplying Expressions: FOIL

Solving Equations: The square root and square cancel

Opposite vs. reciprocal vs. inverse

Beyond teaching in her Massachusetts public high school,
Cardone participates in professional development activities
such as the Program in Mathematics for Young Scientists
(PROMYS), Park City Mathematics Institute (PCMI), and Twitter
Math Camp. To contribute to the final document's formatting,
tagging, illustrating, and more, scroll down her blog post of
Saturday and complete the two-question survey:

"Now that the summer is coming to an end, I keep reminiscing
about all the schoolwork I used to have to complete over the
summer to get me ready for the next and upcoming grade. Every
summer I would have a summer reading book to read. I hardly
ever had math work to complete...."

The National Council of Teachers of Mathematics (NCTM) has just
released a new book all about the distributive property.

Each essay in the collection Insights into Mathematical
Thought: Excursions with Distributivity "encourages readers to
find new ways of understanding the significance and limitations
of a subject usually presented as purely logical and not often
connected with how the mind works in other domains."

Freely sample the table of contents and preface from the
book — available in print or digitally — as well as an
excerpt of the first seven pages of the opening chapter, titled
"Multiple Ways of Seeing." To save up to 25% on purchases, key
in the code that NCTM posted on Facebook:

"I'm at a loss of words to describe the 'proofs' presented in
Geometry Module 1. The lack of rigor in notation drives me
nuts. There are several things about the CCSS I like, even
defining congruence via rigid motions; but having to unlearn a
course I've taught for so long with so much emphasis on rigor
is going to be very difficult. What do the rest of you think?"

- Ronald, posted to the secondary (grades 9-12) discussion
group of the Association of Math Teachers of New York State

The U.S. Census Bureau recently released the first interactive
tool geared exclusively for the nation's congressional
districts — and it comes with a nifty widget.

My Congressional District serves detailed demographic, social,
and economic statistics about the country's 435 districts. The
education category, in particular, breaks out school enrollment
and educational attainment information.

Using the latest annual statistics from the American Community
Survey, the Census' app lets you take data about a selected
113th congressional district and embed them on your own
webpage. Just click "Download and Share" in the app's lower
right corner, then "Embed Widget" above the words "My
Congressional District."

This newsletter is provided as a service of The Math Forum, an online educational community for mathematics hosted by Drexel University, Philadelphia, PA.

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